Tires would vibrate regardless of engine load. It sounds like one of 2 things...engine/transmission mounts, or a worn CV axle. Both can seemingly give you the same symptoms. The thing that I've found tells me it's a bad CV is that the vibration gets worse on one side when steering under load, like taking a right-hand curve uphill. An worn engine or transmission mount can cause vibrations under load as well, and won't always be dependent on which side the weight of the car shifts...these are the cheaper and easier of the two issues to replace. Might be worth a shot to replace the mounts first and see if it gets better. Even if the mounts are not the issue, your engine will feel a lot smoother when you do find the problem.
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